Answer
$a_{1} = 75, r= \frac{1}{5}$
Work Step by Step
Given
$a_{2} = 15$
$a_{3} = 3$
In geometric progression, common ratio,
$r = \frac{a_{n}}{a_{n-1}}$
$r = \frac{a_{3}}{a_{2}} = \frac{3}{15} = \frac{1}{5}$
$a_{2} = a_{1} . r^{2-1} $ using $a_{n} = a_{1} . r^{n-1} $
$a_{2} = a_{1} . r^{1} $
Using $r$ and $a_{2}$ values,
$15 = a_{1} .(\frac{1}{5})^{1} $
$15 = a_{1} .(\frac{1}{5}) $
$a_{1} = 15 \times 5 $
$a_{1} = 75$
